This paper describes non-intrusive performance testing and second law, exergy-based, performance evaluation of a small, contemporary domestic freezer that used R600a refrigerant.
The methodology presented is associated with logging of temperatures and the instantaneous power consumption. It gives a ‘second law of thermodynamics’ perspective on operating performance by providing rational efficiency values and by localizing and quantifying the instantaneous exergy destruction rates.
This approach is compared to a more conventional ‘first law’ energy analysis. Suggestions are made for the standardization of such an approach in order to enhance the sustainability of domestic freezers.
Figure 4 shows test readings taken at one minute intervals for a twenty minute period that was towards the end of a twenty-four test. The figure includes one full cycle that starts at 23 minutes and ends at 34 minutes.
Taking the five cycles, including this one, that start at 0 minutes and finish at 58 minutes, the average ambient temperature was 19.5°C and the average temperature of the frozen water in the bottles was -20.4°C. These temperatures were steady. The average power consumption was 12.8 W.
The test measurements showed that a very steady temperature of the frozen water in the bottles was maintained, while the air temperature within the freezer fluctuated by about 3K for each on-off-on cycle of the compressor. Based on the average power consumption at the stated conditions, the annual energy consumption would be 112 kWh.
SECOND LAW PERFORMANCE
The electric power input to a freezer is equivalent to a rate of exergy input. The rate of exergy transfer X associated with a rate of heat transfer Q at absolute temperature T is given by Equation (2), where 0T is the absolute temperature of the environment. The rational efficiency of the freezer is given by Equation (3), where Tfr is the absolute temperature of the items stored within it.
DEDUCTIONS FROM TEST READINGS
The logged temperature measurements and instantaneous power measurements, together with software for thermodynamic properties, allowed detailed information to be deduced with reasonable accuracy.
The saturation temperatures and hence pressures in the evaporator and condenser were implied from thermocouple measurements at positions where the refrigerant was in the saturated mixture state.
Energy and exergy balances were applied to systems and subsystems that underwent no net change. For instance, the compressor and condenser undergo no net change for an integral number of complete on/off cycles of the compressor, once an unchanging pattern has been established.
Rough Estimates for the Refrigerant Cycle:
Owing to the absence of any mass flow rate measurements, it was not possible to achieve precision in analysing the refrigeration cycle. However,it was possible to make some useful rough estimates.
The logged measurements indicated that the on/off cycles were highly consistent. However, as the data-logging time interval was one minute and the cycle period was about 11 minutes, it was necessary to use multiple cycles to estimate the average values of power input and temperature to reduce errors associated with the sampling interval.
Overall Isentropic Efficiency:
Table 2 compares key operating parameters of the compressor, at the ASHRAE rating point and while the compressor was running.
The Cycle while Running:
The cycle while the compressor was running (Table 2) was used to estimate the average refrigerant mass flow rate while the compressor was running as 610178−× kg/s. This was done by solving for the unknown mass flow rate in Equation (4), on the assumption that the overall isentropic efficiency of the compressor was the same as at the rating point. It is important to appreciate that the energy of a compressor changes while it runs intermittently, as does the amount of refrigerant it contains.
THE EQUIVALENT AVERAGE CYCLE
The equivalent mass flow rate of refrigerant for an integral number of on/off cycles was calculated by multiplying the average mass flow rate while running by the run-time fraction. This equivalent mass flow rate was 6106.73−× kg/s.
COMPARISON OF FIRST AND SECOND LAW APPROACHES
It needs to be stated that the first and second law approaches are not alternatives, but rather support one another as a means of assessing and quantifying the performance of a domestic freezer.
Whereas the compressor had a nominal COP of 1.4 at its rating point, in practice the real refrigeration cycle had a COP of 1.97, or the freezer had COP for meeting the effective heat gain through its insulation of 1.08. The difference between the latter two COPs is because the evaporator on the inside of the cabinet and the condenser on its outside cause additional heat gain, which also must be countered by the refrigeration system.
The elaboration of the methodology described herein was taken on by the first author as a kind of personal challenge. It was met only by pushing the terms of reference further than originally intended. The second author under-took the experimentation within the scope of a thesis project in partial fulfilment of the requirements for a master’s degree.
The methods described here for second law performance evaluation can be applied to fridges or freezers to construct progressively more detailed analyses of where exergy is destroyed and to localize exergy destruction rates along the paths of energy flow within them.
The same techniques can be incorporated in detailed simulation models for design and development and this can enhance the sustainability of these devices. In the absence of better information, the overall isentropic efficiency of a hermetic compressor is a useful parameter that may not vary too greatly over a range of operating conditions.
Source: Dublin Institute of Technology
Authors: Jim Mc Govern | S. Oladunjoye